 5.4.1: Suppose that F (x) = f (x) and F (0) = 3, F (2) = 7. (a) What is th...
 5.4.2: Suppose that f is a negative function with antiderivative F such th...
 5.4.3: Are the following statements true or false?Explain (a) FTC I is val...
 5.4.4: Evaluate 9 2 f (x) dx, where f is differentiable and f (2) = f (9) ...
 5.4.5: In Exercises 542, evaluate the integral using FTC I. 5. 6 3 x dx
 5.4.6: In Exercises 542, evaluate the integral using FTC I.9 0 2 dx
 5.4.7: In Exercises 542, evaluate the integral using FTC I.1 0 (4x 9x2)dx
 5.4.8: In Exercises 542, evaluate the integral using FTC I.2 3 u2 du
 5.4.9: In Exercises 542, evaluate the integral using FTC I.2 0 (12x5 + 3x2...
 5.4.10: In Exercises 542, evaluate the integral using FTC I.2 2 (10x9 + 3x5)dx
 5.4.11: In Exercises 542, evaluate the integral using FTC I.0 3 (2t 3 6t 2)dt
 5.4.12: In Exercises 542, evaluate the integral using FTC I.1 1 (5u4 + u2 u...
 5.4.13: In Exercises 542, evaluate the integral using FTC I.4 0 y dy
 5.4.14: In Exercises 542, evaluate the integral using FTC I.8 1 x4/3 dx
 5.4.15: In Exercises 542, evaluate the integral using FTC I.1 1/16 t 1/4 dt
 5.4.16: In Exercises 542, evaluate the integral using FTC I.1 4 t 5/2 dt
 5.4.17: In Exercises 542, evaluate the integral using FTC I.3 1 dt t2
 5.4.18: In Exercises 542, evaluate the integral using FTC I.4 1 x4 dx
 5.4.19: In Exercises 542, evaluate the integral using FTC I.1 1/2 8 x3 dx
 5.4.20: In Exercises 542, evaluate the integral using FTC I.1 2 1 x3 dx
 5.4.21: In Exercises 542, evaluate the integral using FTC I.2 1 (x2 x2)dx
 5.4.22: In Exercises 542, evaluate the integral using FTC I.9 1 t 1/2 dt
 5.4.23: In Exercises 542, evaluate the integral using FTC I.27 1 t + 1 t dt
 5.4.24: In Exercises 542, evaluate the integral using FTC I.1 8/27 10t4/3 8...
 5.4.25: In Exercises 542, evaluate the integral using FTC I.3/4 /4 sin d
 5.4.26: In Exercises 542, evaluate the integral using FTC I.4 2 sin x dx
 5.4.27: In Exercises 542, evaluate the integral using FTC I./2 0 cos1 3 d
 5.4.28: In Exercises 542, evaluate the integral using FTC I.5/8 /4 cos 2x dx
 5.4.29: In Exercises 542, evaluate the integral using FTC I./6 0 sec2 3t 6 dt
 5.4.30: In Exercises 542, evaluate the integral using FTC I./6 0 sec tan d
 5.4.31: In Exercises 542, evaluate the integral using FTC I./10 /20 csc 5x ...
 5.4.32: In Exercises 542, evaluate the integral using FTC I./14 /28 csc2 7y dy
 5.4.33: In Exercises 542, evaluate the integral using FTC I.1 0 ex dx
 5.4.34: In Exercises 542, evaluate the integral using FTC I.5 3 e4x dx
 5.4.35: In Exercises 542, evaluate the integral using FTC I.3 0 e16t dt
 5.4.36: In Exercises 542, evaluate the integral using FTC I.3 2 e4t3 dt
 5.4.37: In Exercises 542, evaluate the integral using FTC I.10 2 dx x
 5.4.38: In Exercises 542, evaluate the integral using FTC I.4 12 dx x
 5.4.39: In Exercises 542, evaluate the integral using FTC I.1 0 dt t + 1
 5.4.40: In Exercises 542, evaluate the integral using FTC I.4 1 dt 5t + 4
 5.4.41: In Exercises 542, evaluate the integral using FTC I.0 2 (3x 9e3x )dx
 5.4.42: In Exercises 542, evaluate the integral using FTC I.6 2 x + 1 x dx
 5.4.43: In Exercises 4348, write the integral as a sum of integrals without...
 5.4.44: In Exercises 4348, write the integral as a sum of integrals without...
 5.4.45: In Exercises 4348, write the integral as a sum of integrals without...
 5.4.46: In Exercises 4348, write the integral as a sum of integrals without...
 5.4.47: In Exercises 4348, write the integral as a sum of integrals without...
 5.4.48: In Exercises 4348, write the integral as a sum of integrals without...
 5.4.49: In Exercises 4954, evaluate the integral in terms of the constants....
 5.4.50: In Exercises 4954, evaluate the integral in terms of the constants....
 5.4.51: In Exercises 4954, evaluate the integral in terms of the constants....
 5.4.52: In Exercises 4954, evaluate the integral in terms of the constants....
 5.4.53: In Exercises 4954, evaluate the integral in terms of the constants....
 5.4.54: In Exercises 4954, evaluate the integral in terms of the constants....
 5.4.55: Calculate 3 2 f (x) dx, where f (x) = 12 x2 for x 2 x3 for x > 2
 5.4.56: Calculate 2 0 f (x) dx, where f (x) = cos x for x cos x sin 2x for x>
 5.4.57: Use FTC I to show that 1 1 xn dx = 0 if n is an odd whole number. E...
 5.4.58: Plot the function f (x) = sin 3x x. Find the positive root of f to ...
 5.4.59: CalculateF (4) given thatF (1) = 3 andF (x) = x2. Hint:Express F (4...
 5.4.60: Calculate G(16), where dG/dt = t 1/2 and G(9) = 5.
 5.4.61: Does 1 0 xn dx get larger or smaller as n increases? Explain graphi...
 5.4.62: Show that the area of the shaded parabolic arch in Figure 8 is equa...
 5.4.63: Prove a famous result of Archimedes (generalizing Exercise 62): For r
 5.4.64: (a) Apply the Comparison Theorem (Theorem 5 in Section 5.2) to the ...
 5.4.65: Use the method of Exercise 64 to prove that 1 x2 2 cos x 1 x2 2 + x...
 5.4.66: Calculate the next pair of inequalities for sin x and cos x by inte...
 5.4.67: Use FTC I to prove that if f (x) K for x [a, b], then f (x) f (a...
 5.4.68: (a) Use Exercise 67 to prove that sin a sin ba b for all a, b. ...
Solutions for Chapter 5.4: The Fundamental Theorem of Calculus, Part I
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 5.4: The Fundamental Theorem of Calculus, Part I
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.4: The Fundamental Theorem of Calculus, Part I includes 68 full stepbystep solutions. Since 68 problems in chapter 5.4: The Fundamental Theorem of Calculus, Part I have been answered, more than 41580 students have viewed full stepbystep solutions from this chapter.

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Exponential regression
A procedure for fitting an exponential function to a set of data.

Inverse tangent function
The function y = tan1 x

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Multiplicative identity for matrices
See Identity matrix

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Partial sums
See Sequence of partial sums.

Polar equation
An equation in r and ?.

Position vector of the point (a, b)
The vector <a,b>.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Quartic regression
A procedure for fitting a quartic function to a set of data.

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Reflection
Two points that are symmetric with respect to a lineor a point.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Speed
The magnitude of the velocity vector, given by distance/time.